Read the following information carefully and answer the questions given below.

Given that $${\log _x}y,\,{\log _z}x,\,{\log _y}z$$ are in GP, xyz = 64 and x³, y³ and z³ are in AP.

Which one of the following is correct?

xy, yz and zx are

The value of the product $${6^{{1 \over 2}}} \times {6^{{1 \over 4}}} \times {6^{{1 \over 8}}} \times {6^{{1 \over {16}}}} \times ....$$ up to infinite terms is

A person is to count 4500 notes. Let a_n denote the number of notes he counts in the n^th minute.

If a₁ = a₂ = a₃ = ...... = a₁₀ = 150, and a₁₀, a₁₁, a₁₂, ..... are in AP with the common difference $$-$$2, then the time taken by him to count all the notes is

If $$y = x + {x^2} + {x^3} + ...$$ up to infinite terms where x < 1, then which one of the following is correct?